This page has a collection of resources from a talk given at the 2014 CS4HS workshop at the University of
Washington.

There seems to be an increasing awareness that it is important for students to
be able to make what are known as back of
the envelope calculations or ballparking. This fits in with a general
goal of developing number
sense on the part of our students.

How many gas stations are there in the US? (Microsoft interview
question)

Making the totally unreasonable assumption that an ordinary sheet of
paper could be folded in half an indefinite number of times, each time
doubling its thickness, how many times would you have to fold a single
sheet of paper in half until it was thick enough to reach from the Earth
to the Sun?

How many hotels are there in the US? (Google interview question)

How many cows are there in Canada? (Google interview question)

How long would it take to sort 1 trillion numbers? (Google interview
question)

How many golf balls can fit in a school bus? (Google interview
question)

How many flights leave SeaTac airport every day?

How many piano tuners are there in the entire world?

How many slices of pizza do college students in the US consume each
month?

How many contestants have appeared on the TV show "The Price is Right"?
In other words, how many times has the announcer on that show told
someone from the audience to "Come on down."

Our colleague Hélène Martin reports that colleagues of hers at
Garfield got some interesting results from a challenge asking students to
approximate the amount of candy in a jar. The handout is available here.

Stuart mentioned that his favorite estimating trick is that:

210 ≈ 103

There are many computer science algorithms where the number of steps performed
for an input of size n will be approximately equal to the log2(n). So for a
thousand items, it takes 10 steps. For a million, it takes 20. For a billion,
it takes 30. For a trillion, it takes 40. And so on. We like that kind of
behavior where you have a small number of steps to perform even when the
numbers get very large.

Bonus challenge: Stuart posed a related challenge. Suppose that you were
stranded on a desert island and you wanted to have a log table. Not a physical
table made out of logs, although that would seem more practical. We want a
table showing the logarithm in base 10 for the numbers 1 through 10. If you
didn't have a calculator or computer or slide rule or math book with you, how
could you compute the logs in base 10? Two are really easy (the logs of 1 and
10). And one of them is easy given Stuart's favorite approximation mentioned
above. And how do you get the others? Hint: the number 7 isn't very friendly
(old math joke: Why is 6 afraid of 7? Because 7 8 9), but the square of 7 is
your friend if you're thinking about approximations (what is it close to?).
Stuart's answer can be found here.

Computer scientists are more oriented towards integers and powers of 2, but a
lot of people care about real numbers and natural logarithms. Another
interesting approximation that can be used for powers of e is
that:

e3 ≈ 20

Interestingly enough, since this relates e to a number involving 2 and
10, you can use this approximation in conjunction with the other one to do all
sorts of computations.